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Simplifying x2 + -15x + 47 = 0 Reorder the terms: 47 + -15x + x2 = 0 Solving 47 + -15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-47' to each side of the equation. 47 + -15x + -47 + x2 = 0 + -47 Reorder the terms: 47 + -47 + -15x + x2 = 0 + -47 Combine like terms: 47 + -47 = 0 0 + -15x + x2 = 0 + -47 -15x + x2 = 0 + -47 Combine like terms: 0 + -47 = -47 -15x + x2 = -47 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -47 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -47 + 56.25 Combine like terms: -47 + 56.25 = 9.25 56.25 + -15x + x2 = 9.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (x + -7.5) equal to 3.041381265 and -3.041381265.Subproblem 1
x + -7.5 = 3.041381265 Simplifying x + -7.5 = 3.041381265 Reorder the terms: -7.5 + x = 3.041381265 Solving -7.5 + x = 3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 3.041381265 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 3.041381265 + 7.5 x = 3.041381265 + 7.5 Combine like terms: 3.041381265 + 7.5 = 10.541381265 x = 10.541381265 Simplifying x = 10.541381265Subproblem 2
x + -7.5 = -3.041381265 Simplifying x + -7.5 = -3.041381265 Reorder the terms: -7.5 + x = -3.041381265 Solving -7.5 + x = -3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -3.041381265 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -3.041381265 + 7.5 x = -3.041381265 + 7.5 Combine like terms: -3.041381265 + 7.5 = 4.458618735 x = 4.458618735 Simplifying x = 4.458618735Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.541381265, 4.458618735}
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